L11a383

(Knotscape image)

See the full Thistlethwaite Link Table (up to 11 crossings).

Planar diagram presentation	X_12,1,13,2 X_2,13,3,14 X_14,3,15,4 X_10,11,1,12 X_22,15,11,16 X_16,8,17,7 X_6,22,7,21 X_20,6,21,5 X_4,20,5,19 X_18,10,19,9 X_8,18,9,17
Gauss code	{1, -2, 3, -9, 8, -7, 6, -11, 10, -4}, {4, -1, 2, -3, 5, -6, 11, -10, 9, -8, 7, -5}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$- v 4 u 4 + v 3 u 4 + v 4 u 3 -4 v 3 u 3 + 3 v 2 u 3 + 3 v 3 u 2 -7 v 2 u 2 + 3 v u 2 + 3 v 2 u -4 v u + u + v -1$ (db)
Jones polynomial	$-q^{13/2}+2 q^{11/2}-4 q^{9/2}+7 q^{7/2}-9 q^{5/2}+10 q^{3/2}-11 \sqrt{q}+\frac{8}{\sqrt{q}}-\frac{7}{q^{3/2}}+\frac{4}{q^{5/2}}-\frac{2}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$z 9 a -1 - a z 7 + 8 z 7 a -1 - z 7 a -3 -6 a z 5 + 24 z 5 a -1 -6 z 5 a -3 -12 a z 3 + 32 z 3 a -1 -12 z 3 a -3 -8 a z + 17 z a -1 -8 z a -3 + a -1 z -1 - a -3 z -1$ (db)
Kauffman polynomial	$- z 10 a -2 - z 10 -2 a z 9 -5 z 9 a -1 -3 z 9 a -3 -2 a 2 z 8 - z 8 a -2 -4 z 8 a -4 + z 8 -2 a 3 z 7 + 7 a z 7 + 23 z 7 a -1 + 11 z 7 a -3 -3 z 7 a -5 - a 4 z 6 + 5 a 2 z 6 + 14 z 6 a -2 + 15 z 6 a -4 -2 z 6 a -6 + 3 z 6 + 7 a 3 z 5 -15 a z 5 -49 z 5 a -1 -18 z 5 a -3 + 8 z 5 a -5 - z 5 a -7 + 4 a 4 z 4 -2 a 2 z 4 -31 z 4 a -2 -22 z 4 a -4 + 5 z 4 a -6 -10 z 4 -6 a 3 z 3 + 22 a z 3 + 47 z 3 a -1 + 11 z 3 a -3 -5 z 3 a -5 + 3 z 3 a -7 -4 a 4 z 2 + a 2 z 2 + 16 z 2 a -2 + 10 z 2 a -4 - z 2 a -6 + 10 z 2 + a 3 z -9 a z -19 z a -1 -7 z a -3 + z a -5 - z a -7 - a -2 + a -1 z -1 + a -3 z -1$ (db)

The coefficients of the monomials

t r q j

are shown, along with their alternating sums

χ

(fixed

j

, alternation over

r

). The squares with yellow highlighting are those on the "critical diagonals", where

j -2 r = s + 1

j -2 r = s -1

, where

s =

1 is the signature of L11a383. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

$\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$	$i = 0$	$i = 2$
$r = -5$	${\mathbb Z}$
$r = -4$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = -2$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = -1$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 0$	${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{5}$
$r = 1$	${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$	${\mathbb Z}^{6}$
$r = 2$	${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{5}$
$r = 3$	${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4}$	${\mathbb Z}^{4}$
$r = 4$	${\mathbb Z}\oplus{\mathbb Z}_2^{3}$	${\mathbb Z}^{3}$
$r = 5$	${\mathbb Z}\oplus{\mathbb Z}_2$	${\mathbb Z}$
$r = 6$	${\mathbb Z}_2$	${\mathbb Z}$